A vestigial structure is a trait that has lost most of its ancestral role or function through evolution.
Vestigial does not mean completely useless. A reduced structure may retain a minor function, serve a new function, or have developmental and physiological effects. In humans, the coccyx is a reduced remnant of an ancestral tail, while the muscles that move the ears have limited roles for most people.
Vestigial traits are evidence of evolutionary history because they can persist after the original selective advantage has diminished. Their presence is especially informative when related species retain a larger or more functional version of the same structure.
A common error is to call every small or unusual organ vestigial. The label requires evidence about ancestry and reduced function, not merely an assumption that the feature has no purpose.